This invention relates generally to a method of and apparatus for determining the capacity of a telecommunications system and in particular to a method and apparatus for use in the presence of non-Gaussian noise.
A common source of noise in, for example, an x-Digital Subscriber loop (xDSL) system that utilises copper cables to send signals is Amplitude Modulated (AM) signals from Broadcast Radio in the Medium Wave Band (MW). These noise signals reside in the centre of the transmission bands of both Asymmetric Digital Subscriber Loop (ADSL) and Very High Speed Digital Subscriber Loop (VDSL) systems.
These signals typically have a modulation Index of 80%, which is predominantly sinusoidal in its Probability Density Function (PDF). It will be shown below that using solely the RMS value of this noise and assuming it to be Gaussian in its PDF, as with prior art methods, will severely underestimate the available capacity of a telecommunications system.
One of the problems addressed by the invention is, how to calculate the available capacity in, for example, a Quadrature Amplitude Modulation (QAM) based modulation system more accurately than previously used methods. In order to address this problem the signal to noise ratio for a carrier needs to be measured differently.
The usual measure of Signal to Noise (SNR) ratio is the root mean square (RMS) value of the noise at the carrier frequency. This, however, does not indicate any other property of the noise such as its peak value, which is a crucial property for error free performance. If the type of noise is known, then from its probability density function (PDF), a relationship between its RMS value and the probability of a peak can be obtained. In the case of Gaussian noise, however, in principal the peak size may be infinite.
The metric used, therefore, is the peak level that occurs with a given level of probability, which corresponds to a particular error rate for the xDSL system. For instance, for measurement purposes, it is common to use a Bit Error Rate (BER) of 1 in [1e7] 107. The ratio of the peak level and the RMS value is about 5.3 or 14.5 dB for Gaussian noise. For sinusoidal noise, however, the peak to RMS ratio is 1.414 (square root of 2) or 3 dB. The difference between the two types of noise is therefore 11.5 dB. Therefore, the assumption that noise is Gaussian has lead, in presently used methods, to an over estimation of the noise in the system and consequently to an under utilisation of actual available capacity.
FIGS. 1 and 2 illustrate a Gaussian noise signal and a sinusoidal noise signal such as that presented by an AM signal, and their PDF, respectively.
For example in QAM modulation, 3 dB of SNR are required for each bit. Thus for a given level of RMS noise, nearly 4 extra bits are possible if the noise is sinusoidal. In a multi-carrier system where bits are allocated during training, such as in Coded Orthogonal Frequency Division Multiplexing (COFDM), there is therefore significant benefit if the type of noise can be measured when allocating the maximum number of bits to a carrier.
It is an object of the present invention to address the problem of the over-estimation of noise in a telecommunications system and the resultant under-utilisation of available capacity.
It is a further object of the present invention to distinguish between Gaussian and non-Gaussian noise in a telecommunications system.
According to a first aspect of the present invention there is provided a method of determining the capacity of a telecommunications system, in the presence of Gaussian and non-Gaussian noise, wherein the ratio of Gaussian to non-Gaussian noise is determined utilising a statistical metric.
According to a second aspect of the present invention there is provided a telecommunications apparatus for use in a telecommunications system, in the presence of Gaussian and non-Gaussian noise, comprising a processor arranged to determine the capacity of the system by determining the ratio of Gaussian to non-Gaussian Noise utilising a statistical metric.
Preferably, the apparatus is an xDSL modem.
According to a third aspect of the present invention there is provided a method of bit allocation in a telecommunications system, in the presence of Gaussian and non-Gaussian noise, wherein the ratio of Gaussian to non-Gaussian noise is determined utilising a statistical metric.
According to a fourth aspect of the present invention there is provided a computer program product stored on a computer readable medium, having thereon computer program means for causing a computer which governs the operation of a telecommunications apparatus in a telecommunications system, in the presence of Gaussian and non-Gaussian noise, to determine the capacity of the system by determining the ratio of Gaussian to non-Gaussian Noise utilising a statistical metric
Preferably, the statistical metric is the Kurtosis of the Probability Density of the signal at each frequency.
Alternatively, the statistical metric is the 3rd Cumulant of the Probability Density of the signal at each frequency.
Preferably, the telecommunications system utilises a modulation scheme selected from the following: Quadrature Amplitude Modulation (QAM); OFDM or COFDM
It is an advantage of the present invention that the capacity issue is addressed by using other statistical metrics as well as the RMS (standard deviation) to estimate the available capacity. This is in stark contrast to prior art bit allocation and capacity management methods in which only the RMS value has been used to estimate the bit SNR and hence the available capacity.